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Bài tập 19 trang 154 Tài liệu dạy – học Toán 7 tập 1

Giải bài tập Cho góc xOy và tia Mn
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Đề bài

Cho góc xOy và tia Mn Vẽ cung tròn tâm O bán kính 3 cm, cung này cắt Ox, Oy theo thứ tự tại H, I. Vẽ cung tròn tâm M bán kính 3 cm, cung này cắt tia Mn ở E. Vẽ cung trong tâm E bán kính bằng IH, cung này cắt cung tròn tâm M bán kính 3 cm tại G. Chứng minh rằng: \(\widehat {EMG} = \widehat {xOy}\)

 

* Chú ý: Bài toán này cho ta cách dùng thước và compa vẽ một góc bằng góc cho trước.

Lời giải chi tiết

Xét tam giác OHI và MGE có:OH = MG (=3cm)OI = ME (=3cm)IH = GEDo đó: \(\Delta OHI = \Delta MGE(c.c.c) \Rightarrow \widehat {HOI} = \widehat {GME}hay\widehat {xOy} = \widehat {GME}\)

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